Lepton flavour and neutrino mass aspects of the Ma-model

Alexander MerleMax-Planck-Institute for Nuclear Physics

Heidelberg, Germany

Based on:Adulpravitchai, Lindner, AM: Confronting Flavour Symmetries and extended Scalar Sectors with Lepton Flavour Violation Bounds, Phys. Rev. D80 (2009) 055031

Adulpravitchai, Lindner, AM, Mohapatra: Radiative Trans-mission of Lepton Flavor Hierarchies, Phys. Lett. B680 (2009) 476 - 479

Southampton, Friday Seminar, October 30, 2009

Contents:

1. Introduction

2. The Ma-model

3. Flavour and the Ma-model

4. The LR-extension of the Ma-model

5. Conclusions

1. Introduction: Particle masses

• the masses of the Standard Model particles seem to increase with the generation number

• HOWEVER: neutrinos have masses that are (at least) a factor of 106 smaller than the one of the electron → neutrino masses do not seem to have the same origin as the other masses

• there are different possibilities to generate small neutrino masses

• the masses of the Standard Model particles seem to increase with the generation number

• HOWEVER: neutrinos have masses that are (at least) a factor of 106 smaller than the one of the electron → neutrino masses do not seem to have the same origin as the other masses

• there are different possibilities to generate small neutrino masses

• the masses of the Standard Model particles seem to increase with the generation number

• HOWEVER: neutrinos have masses that are (at least) a factor of 106 smaller than the one of the electron → neutrino masses do not seem to have the same origin as the other masses

• there are different possibilities to generate small neutrino masses

Tree-level diagrams: e.g. seesaw type I

Tree-level diagrams: e.g. seesaw type I

Tree-level diagrams: e.g. seesaw type I

good: “natural” value for the Yukawa coupling “natural” explanation for large MR

bad: scale for MR is arbitrary

Radiative masses: e.g. Zee/Wolfenstein model

Radiative masses: e.g. Zee/Wolfenstein model

Radiative masses: e.g. Zee/Wolfenstein model

good: neutrino mass loop suppressed

bad: this model is ruled out…

2. Ma’s scotogenic model (Ma-model)

2. Ma’s scotogenic model (Ma-model)

Ingredients apart from the SM:

• 3 heavy right-handed Majorana neutrinos Nk (SM singlets)

• second Higgs doublet η without VEV (with SM-like quantum numbers)

• additional Z2-parity, under which all particles are even except for Nk and η

2. Ma’s scotogenic model (Ma-model)

Ingredients apart from the SM:

• 3 heavy right-handed Majorana neutrinos Nk (SM singlets)

• second Higgs doublet η without VEV (with SM-like quantum numbers)

• additional Z2-parity, under which all particles are even except for Nk and η

2. Ma’s scotogenic model (Ma-model)

Ingredients apart from the SM:

• 3 heavy right-handed Majorana neutrinos Nk (SM singlets)

• second Higgs doublet η without VEV (with SM-like quantum numbers)

• additional Z2-parity, under which all particles are even except for Nk and η

2. Ma’s scotogenic model (Ma-model)

Ingredients apart from the SM:

• 3 heavy right-handed Majorana neutrinos Nk (SM singlets)

• second Higgs doublet η without VEV (with SM-like quantum numbers)

• additional Z2-parity, under which all particles are even except for Nk and η

Features of the Ma-model:

• relatively minimal extension of the SM (essentially a 2HDM)

• Z2-parity plays a similar role as R-parity in SUSY → stable Dark matter candidates: neutral scalar η0 or lightest heavy Neutrino N1

• tree-level neutrino mass vanishes → generated at 1 loop

Features of the Ma-model:

• relatively minimal extension of the SM (essentially a 2HDM)

• Z2-parity plays a similar role as R-parity in SUSY → stable Dark matter candidates: neutral scalar η0 or lightest heavy Neutrino N1

• tree-level neutrino mass vanishes → generated at 1 loop

Features of the Ma-model:

• relatively minimal extension of the SM (essentially a 2HDM)

• Z2-parity plays a similar role as R-parity in SUSY → stable Dark matter candidates: neutral scalar η0 or lightest heavy Neutrino N1

• tree-level neutrino mass vanishes → generated at 1 loop

Features of the Ma-model:

• relatively minimal extension of the SM (essentially a 2HDM)

• Z2-parity plays a similar role as R-parity in SUSY → stable Dark matter candidates: neutral scalar η0 or lightest heavy Neutrino N1

• tree-level neutrino mass vanishes → generated at 1 loop

The Ma-model neutrino mass:

The Ma-model neutrino mass:

Yukawa coupling:

The Ma-model neutrino mass:

Yukawa coupling:

This part would lead to a neutrino mass.

BUT: ‹η0›=0

→ tree-level contribution vanishes

The Ma-model neutrino mass:

Yukawa coupling:

This part would lead to a neutrino mass.

BUT: ‹η0›=0

→ tree-level contribution vanishes

Leading order: 1-loop diagram

Leading order: 1-loop diagram

Leading order: 1-loop diagram

Leading order: 1-loop diagram

Leading order: 1-loop diagram

Light neutrino mass matrix:

Light neutrino mass matrix:

Light neutrino mass matrix:

Light neutrino mass matrix:

Higgs masses:

Light neutrino mass matrix:

Features:

• “natural” Yukawa couplings

• loop suppression 1/(16π2)

• radiative seesaw → TeV-scale heavy neutrinos

Light neutrino mass matrix:

Features:

• “natural” Yukawa couplings

• loop suppression 1/(16π2)

• radiative seesaw → TeV-scale heavy neutrinos

Light neutrino mass matrix:

Features:

• “natural” Yukawa couplings

• loop suppression 1/(16π2)

• radiative seesaw → TeV-scale heavy neutrinos

Light neutrino mass matrix:

Features:

• “natural” Yukawa couplings

• loop suppression 1/(16π2)

• radiative seesaw → TeV-scale heavy neutrinos

3. Flavour and the Ma-model:

3. Flavour and the Ma-model:

The Yukawa coupling that enters into the neutrino mass also generates LFV processes:

3. Flavour and the Ma-model:

The Yukawa coupling that enters into the neutrino mass also generates LFV processes:

3. Flavour and the Ma-model:

The Yukawa coupling that enters into the neutrino mass also generates LFV processes:

LFV-processes are strongly constrained (MEGA experiment):

LFV-processes are strongly constrained (MEGA experiment):

BUT: these bounds only constrain combinations of Yukawa coupling elements → cancellations possible → no problem for the Ma-model

LFV-processes are strongly constrained (MEGA experiment):

BUT: these bounds only constrain combinations of Yukawa coupling elements → cancellations possible → no problem for the Ma-model

What will happen if a (discrete) flavour symmetry is imposed?

What will happen if a (discrete) flavour symmetry is imposed?

• without symmetry, the combination of Yukawa coupling matrix elements can be zero

• a flavour symmetry imposes structure on the Yukawa matrix → easy example: h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0 → then, the above amounts to: 3|a|2 → trivial or non-zero → may get in conflict with the constraints

What will happen if a (discrete) flavour symmetry is imposed?

• without symmetry, the combination of Yukawa coupling matrix elements can be zero

• a flavour symmetry imposes structure on the Yukawa matrix → easy example: h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0 → then, the above amounts to: 3|a|2 → trivial or non-zero → may get in conflict with the constraints

What will happen if a (discrete) flavour symmetry is imposed?

• without symmetry, the combination of Yukawa coupling matrix elements can be zero

• a flavour symmetry imposes structure on the Yukawa matrix → easy example: h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0 → then, the above amounts to: 3|a|2 → trivial or non-zero → may get in conflict with the constraints

What will happen if a (discrete) flavour symmetry is imposed?

• without symmetry, the combination of Yukawa coupling matrix elements can be zero

• a flavour symmetry imposes structure on the Yukawa matrix → easy example: h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0 → then, the above amounts to: 3|a|2 → trivial or non-zero → may get in conflict with the constraints

What will happen if a (discrete) flavour symmetry is imposed?

• without symmetry, the combination of Yukawa coupling matrix elements can be zero

• a flavour symmetry imposes structure on the Yukawa matrix → easy example: h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0 → then, the above amounts to: 3|a|2 → trivial or non-zero → may get in conflict with the constraints

What will happen if a (discrete) flavour symmetry is imposed?

• without symmetry, the combination of Yukawa coupling matrix elements can be zero

• a flavour symmetry imposes structure on the Yukawa matrix → easy example: h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0 → then, the above amounts to: 3|a|2 → trivial or non-zero → may get in conflict with the constraints

What will happen if a (discrete) flavour symmetry is imposed?

• without symmetry, the combination of Yukawa coupling matrix elements can be zero

• a flavour symmetry imposes structure on the Yukawa matrix → easy example: h11=h12=h13=h21=h22=h23=a, h31=h32=h33=0 → then, the above amounts to: 3|a|2 → trivial or non-zero → may get in conflict with the constraints

Key points (for multi-scalar models):

• the Yukawa coupling elements are not arbitrary:

- flavour symmetry imposes structure

- correct neutrino masses required

- Dark Matter abundance has to be correct (BUT: this depends on the DM-candidate)

• these ingredients are easily sufficient to destroy the models consistency with LFV-constraints!

Key points (for multi-scalar models):

• the Yukawa coupling elements are not arbitrary:

- flavour symmetry imposes structure

- correct neutrino masses required

- Dark Matter abundance has to be correct (BUT: this depends on the DM-candidate)

• these ingredients are easily sufficient to destroy the models consistency with LFV-constraints!

Key points (for multi-scalar models):

• the Yukawa coupling elements are not arbitrary:

- flavour symmetry imposes structure

- correct neutrino masses required

- Dark Matter abundance has to be correct (BUT: this depends on the DM-candidate)

• these ingredients are easily sufficient to destroy the models consistency with LFV-constraints!

Key points (for multi-scalar models):

• the Yukawa coupling elements are not arbitrary:

- flavour symmetry imposes structure

- correct neutrino masses required

- Dark Matter abundance has to be correct (BUT: this depends on the DM-candidate)

• these ingredients are easily sufficient to destroy the models consistency with LFV-constraints!

Key points (for multi-scalar models):

• the Yukawa coupling elements are not arbitrary:

- flavour symmetry imposes structure

- correct neutrino masses required

- Dark Matter abundance has to be correct (BUT: this depends on the DM-candidate)

• these ingredients are easily sufficient to destroy the models consistency with LFV-constraints!

Key points (for multi-scalar models):

• the Yukawa coupling elements are not arbitrary:

- flavour symmetry imposes structure

- correct neutrino masses required

- Dark Matter abundance has to be correct (BUT: this depends on the DM-candidate)

• these ingredients are easily sufficient to destroy the models consistency with LFV-constraints!

Two explicit examples:

Two explicit examples:

Model 1: A4 x Z4,aux → very predictive

Two explicit examples:

Model 1: A4 x Z4,aux → very predictive

Two explicit examples:

Model 1: A4 x Z4,aux → very predictive

Two explicit examples:

Model 1: A4 x Z4,aux → very predictive

Two explicit examples:

Model 1: A4 x Z4,aux → very predictive

3 free parameters: a, b, M

Two explicit examples:

Model 2: D4 x Z2,aux → less predictive

Two explicit examples:

Model 2: D4 x Z2,aux → less predictive

Two explicit examples:

Model 2: D4 x Z2,aux → less predictive

Two explicit examples:

Model 2: D4 x Z2,aux → less predictive

MR diagonal

Two explicit examples:

Model 2: D4 x Z2,aux → less predictive

7 free parameters: a, b, c, d, M1, M2, M3

MR diagonal

Constraints on the Higgs sector with η0 as DM:

Constraints on the Higgs sector with η0 as DM:

• DM: only a few parameter ranges lead to the correct abundance

• ρ-parameter

• decay widths of W± and Z0 & collider limits

• stability & consistency

Constraints on the Higgs sector with η0 as DM:

• DM: only a few parameter ranges lead to the correct abundance

• ρ-parameter

• decay widths of W± and Z0 & collider limits

• stability & consistency

Constraints on the Higgs sector with η0 as DM:

• DM: only a few parameter ranges lead to the correct abundance

• ρ-parameter

• decay widths of W± and Z0 & collider limits

• stability & consistency

Constraints on the Higgs sector with η0 as DM:

• DM: only a few parameter ranges lead to the correct abundance

• ρ-parameter

• decay widths of W± and Z0 & collider limits

• stability & consistency

Constraints on the Higgs sector with η0 as DM:

• DM: only a few parameter ranges lead to the correct abundance

• ρ-parameter

• decay widths of W± and Z0 & collider limits

• stability & consistency

→ 4 scenarios:

Then, one can fit the neutrino data:

Then, one can fit the neutrino data:

Model 1:

Then, one can fit the neutrino data:

Model 2:Model 1:

Then, one can fit the neutrino data:

Model 2:Model 1:

Example: Model 1 & Scenario α

Example: Model 1 & Scenario α

• Method: χ2-fit

Example: Model 1 & Scenario α

• Method: χ2-fit

• Best-fit parameters: model fits neutrino data

Example: Model 1 & Scenario α

• Method: χ2-fit

• Best-fit parameters: model fits neutrino data

• 1σ- and 3σ-ranges: quite narrow

LFV: ei→ejγ and μ-e conversion

LFV: ei→ejγ and μ-e conversion

LFV: ei→ejγ and μ-e conversion

LFV: ei→ejγ and μ-e conversion

Results for Model 1 (A4-model, 3 D.O.F.):

Results for Model 1 (A4-model, 3 D.O.F.):

Results for Model 1 (A4-model, 3 D.O.F.):

• the model is very predictive (3 params)

• when fitted to neutrino data, this model is already ruled out by μ→eγ

Results for Model 2 (D4-model, 7 D.O.F.):

Results for Model 2 (D4-model, 7 D.O.F.):

Results for Model 2 (D4-model, 7 D.O.F.):

• the model is less predictive (7 params)

• BUT: even this model is (can be) excluded by current (future) data for 2 scenarios

The general principle behind:

The general principle behind:

• any model with an extended scalar sector will lead to flavour changing neutral currents (under “normal” circumstances)

• as LFV only constrains combinations of Yukawa matrix elements, cancellations can always rescue the model

• flavour symmetries impose more structure and can destroy the possibility of cancellations

→ will be true in a much more general context

The general principle behind:

• any model with an extended scalar sector will lead to flavour changing neutral currents (under “normal” circumstances)

• as LFV only constrains combinations of Yukawa matrix elements, cancellations can always rescue the model

• flavour symmetries impose more structure and can destroy the possibility of cancellations

→ will be true in a much more general context

The general principle behind:

• any model with an extended scalar sector will lead to flavour changing neutral currents (under “normal” circumstances)

• as LFV only constrains combinations of Yukawa matrix elements, cancellations can always rescue the model

• flavour symmetries impose more structure and can destroy the possibility of cancellations

→ will be true in a much more general context

The general principle behind:

• any model with an extended scalar sector will lead to flavour changing neutral currents (under “normal” circumstances)

• as LFV only constrains combinations of Yukawa matrix elements, cancellations can always rescue the model

• flavour symmetries impose more structure and can destroy the possibility of cancellations

→ will be true in a much more general context

4. The LR-version of the Ma-model:

4. The LR-version of the Ma-model:

There are still questions left:

4. The LR-version of the Ma-model:

There are still questions left:

• Can the Ma-model be extended to the quark sector?

• Is there an “origin” of the Ma-model structure?

• Can the model be embedded into a GUT?

4. The LR-version of the Ma-model:

There are still questions left:

• Can the Ma-model be extended to the quark sector?

• Is there an “origin” of the Ma-model structure?

• Can the model be embedded into a GUT?

4. The LR-version of the Ma-model:

There are still questions left:

• Can the Ma-model be extended to the quark sector?

• Is there an “origin” of the Ma-model structure?

• Can the model be embedded into a GUT?

4. The LR-version of the Ma-model:

There are still questions left:

• Can the Ma-model be extended to the quark sector?

• Is there an “origin” of the Ma-model structure?

• Can the model be embedded into a GUT?

→ consider a left-right symmetric extension

Particle content:

Particle content:

Particle content:

• scalar bi-doublet: contains the SM-Higgs as well as the inert Higgs η

• Higgs triplets: allow for a symmetry breaking pattern that leads to an effective Ma-model in the lepton sector (LR → Ma → effective SM)

• additional Z4-symmetry → will play the role of an effective Z2-parity in the lepton sector

Particle content:

• scalar bi-doublet: contains the SM-Higgs as well as the inert Higgs η

• Higgs triplets: allow for a symmetry breaking pattern that leads to an effective Ma-model in the lepton sector (LR → Ma → effective SM)

• additional Z4-symmetry → will play the role of an effective Z2-parity in the lepton sector

Particle content:

• scalar bi-doublet: contains the SM-Higgs as well as the inert Higgs η

• Higgs triplets: allow for a symmetry breaking pattern that leads to an effective Ma-model in the lepton sector (LR → Ma → effective SM)

• additional Z4-symmetry → will play the role of an effective Z2-parity in the lepton sector

VEV structure:

VEV structure:

→ like in the Ma-model

VEV structure:

→ like in the Ma-model

→ LR-breaking

VEV structure:

→ like in the Ma-model

→ LR-breaking

→ no tree-level light neutrino mass

VEV structure:

→ like in the Ma-model

→ LR-breaking

→ below SU(2)R x U(1)B-L breaking scale, the model is an effective Ma-like model

→ no tree-level light neutrino mass

The neutrino mass formula:

The neutrino mass formula:

• most general Yukawa coupling:

The neutrino mass formula:

• most general Yukawa coupling:

• key point: the neutrino Yukawa couplings are the same as the ones of the charged leptons

The neutrino mass formula:

• most general Yukawa coupling:

• key point: the neutrino Yukawa couplings are the same as the ones of the charged leptons

→ then, the neutrino mass formula looks like:

The neutrino mass formula:

• most general Yukawa coupling:

• key point: the neutrino Yukawa couplings are the same as the ones of the charged leptons

→ then, the neutrino mass formula looks like:

IMPORTANT: charged lepton masses involved

Plausible assumption for scalar Dark Matter:

Plausible assumption for scalar Dark Matter:

→ this leads to:

Plausible assumption for scalar Dark Matter:

→ this leads to:

The log-term can be absorbed into MN…

Then, the light neutrino mass matrix is given by:

Then, the light neutrino mass matrix is given by:

ml=diag(me,mμ,mτ)

Then, the light neutrino mass matrix is given by:

ml=diag(me,mμ,mτ)

→ everything known except for λ5 and MN

Then, the light neutrino mass matrix is given by:

ml=diag(me,mμ,mτ)

→ everything known except for λ5 and MN

→ with a certain form for the light neutrino mass matrix, it is possible to reconstruct MN!

Then, the light neutrino mass matrix is given by:

ml=diag(me,mμ,mτ)

→ everything known except for λ5 and MN

→ with a certain form for the light neutrino mass matrix, it is possible to reconstruct MN!

→ radiative transmission of hierarchies!

Radiative transmission of hierarchies:

Radiative transmission of hierarchies:

tri-bimaximal form for UPMNS (semi-realistic) → it is possible to reconstruct the heavy neutrino mass matrix:

Radiative transmission of hierarchies:

a

tri-bimaximal form for UPMNS (semi-realistic) → it is possible to reconstruct the heavy neutrino mass matrix:

Radiative transmission of hierarchies:

tri-bimaximal form for UPMNS (semi-realistic) → it is possible to reconstruct the heavy neutrino mass matrix:

→ roughly:

Radiative transmission of hierarchies:

tri-bimaximal form for UPMNS (semi-realistic) → it is possible to reconstruct the heavy neutrino mass matrix:

→ MN has a form that can easily be obtained by the Froggat-Nielsen mechanism!

→ roughly:

Key points:

Key points:

• the hierarchical structure of the charged lepton masses translates a (quasi) Froggat-Nielsen pattern of MN into an anarchical form of the light neutrino mass matrix

• this makes large mixing angles in the lepton sector perfectly possible!

• no flavour symmetry argument is required

Key points:

• the hierarchical structure of the charged lepton masses translates a (quasi) Froggat-Nielsen pattern of MN into an anarchical form of the light neutrino mass matrix

• this makes large mixing angles in the lepton sector perfectly possible!

• no flavour symmetry argument is required

Key points:

• the hierarchical structure of the charged lepton masses translates a (quasi) Froggat-Nielsen pattern of MN into an anarchical form of the light neutrino mass matrix

• this makes large mixing angles in the lepton sector perfectly possible!

• no flavour symmetry argument is required

Key points:

• the hierarchical structure of the charged lepton masses translates a (quasi) Froggat-Nielsen pattern of MN into an anarchical form of the light neutrino mass matrix

• this makes large mixing angles in the lepton sector perfectly possible!

• no flavour symmetry argument is required

→ the radiative transmission is a mechanism that can explain large mixings for leptons

Currently under investigation:

Currently under investigation:

• “problem”: ‹η0›=0 → down quarks massless → two ways out: soft Z2-breaking with colour triplet scalars ωL,R (→ 1-loop d-mass) OR introduction of new vector-like down-quarks

Currently under investigation:

• FCNCs in the quark sector

• “problem”: ‹η0›=0 → down quarks massless → two ways out: soft Z2-breaking with colour triplet scalars ωL,R (→ 1-loop d-mass) OR introduction of new vector-like down-quarks

Currently under investigation:

• FCNCs in the quark sector

• further investigations of radiative transmission

• “problem”: ‹η0›=0 → down quarks massless → two ways out: soft Z2-breaking with colour triplet scalars ωL,R (→ 1-loop d-mass) OR introduction of new vector-like down-quarks

5. Conclusions:

5. Conclusions:

• the Ma-model is an interesting toy with surprisingly many interesting features

• it is the prime example for the fact that extended scalar sectors in combination with flavour symmetries have trouble with LFV

• the LR-extension of the Ma-model even yields a new possibility to simultaneously generate small neutrino masses and large lepton mixings

• hopefully, the surprises will go on…

5. Conclusions:

• the Ma-model is an interesting toy with surprisingly many interesting features

• it is the prime example for the fact that extended scalar sectors in combination with flavour symmetries have trouble with LFV

• the LR-extension of the Ma-model even yields a new possibility to simultaneously generate small neutrino masses and large lepton mixings

• hopefully, the surprises will go on…

5. Conclusions:

• the Ma-model is an interesting toy with surprisingly many interesting features

• it is the prime example for the fact that extended scalar sectors in combination with flavour symmetries have trouble with LFV

• the LR-extension of the Ma-model even yields a new possibility to simultaneously generate small neutrino masses and large lepton mixings

• hopefully, the surprises will go on…

5. Conclusions:

• the Ma-model is an interesting toy with surprisingly many interesting features

• it is the prime example for the fact that extended scalar sectors in combination with flavour symmetries have trouble with LFV

• the LR-extension of the Ma-model even yields a new possibility to simultaneously generate small neutrino masses and large lepton mixings

• hopefully, the surprises will go on…

THANK YOU!!!